Balancing Robustness and Efficiency in Multi-Agent Combinatorial Path Finding with Sum of Service Time

Yehonatan Kidushim, Meir Kalech, Roni Stern, Dor Atzmon, Avraham Natan

Keywords: Multi-Agent Path Finding, Multi-Agent Combinatorial Path Finding, Planning Under Uncertainty

TL;DR: A new algorithm for Multi-Agent Combinatorial Path Finding (MACPF) that minimizes the Sum of Service Times (SST) and is able to handle stochastic delays, balancing offline and online planning.

Abstract:

Consider a system of multiple physical agents tasked with collaboratively collecting a set of spatially distributed goals while avoiding collisions with the environment and with each other.
This type of problem, which combines Multi-Agent Path Finding (MAPF) with task allocation, is known as Multi-Agent Combinatorial Path Finding (MCPF).
Conflict-Based Steiner Search (CBSS) is an optimal algorithm for MCPF, which assumes that each agent has a fixed goal destination. It selects allocations that yield a solution minimizing the sum of costs (SOC), which we denote as CBSS$_{SOC}$.
However, this objective is problematic in domains such as search and rescue, where timely service of all goals is more critical than minimizing SOC.
We therefore propose CBSS$_{SST}$, which minimizes the Sum of Service Times (SST) across all goals using a novel mixed-integer linear programming allocation, thereby generalizing MCPF to settings without requiring fixed goal destinations.
Since CBSS assumes perfect execution, we extend it with robust planning to handle stochastic execution delays.
We propose two variants of CBSS$_{SST}$: Robust CBSS$_{SST}$ with Strict Verifier, which guarantees the desired robustness, and Robust CBSS$_{SST}$ with Anytime Verifier, which addresses planning-time constraints by returning the most robust solution verified within the available time.
Our experiments on MCPF benchmarks show that Robust CBSS with anytime verifier solves substantially more instances than when using a strict verified within the time limit, while reducing replanning effort and preserving robustness.
These results demonstrate that RCbss with an anytime verifier provides an effective and practical approach to MCPF under uncertainty.

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Submission Number: 45